The essence of the CHSP formalism
has most concisely been explained by Mostafazadeh [1]}.
He put emphasis upon the interplay
of the inner-product structures in \({\cal H}_{math/phys}\) .
He emphasized that the
standard physical
role is played by
\({\cal H}_{phys}\) .
Although the merits
of
the introduction of another,
apparently redundant Hilbert space
\({\cal H}_{math}\) 
seem less obvious, its introduction
separated the interpretations
(in \({\cal H}_{phys}\) )
from calculations
(in \({\cal H}_{math}\) ) and facilitated the
qualitative as well as quantitative predictions
(cf., once more, the above-mentioned
Dyson's study of ferromagnetism [2]}).
At the same time,
during
the implementation of the general CHSP theory
people encountered also serious technical obstacles
(some of them were
listed on p. \(1216\ \)  of review
[1]}).
For this reason,
only
the most recent simplifications made the theory
really widely known and
successful [4]}.
